Convert a map distance using a ratio scale

A ratio scale such as 1:50 000 tells you how much smaller the map is than the ground. To find a real distance, measure on the map, multiply by the scale number, then convert the units. It appears in map-skills questions and in the calculation parts of fieldwork and case-study papers.

This is the first lesson in scale, distance and relief. Later lessons on area and gradient reuse the same conversion.

What does a ratio scale tell you?

The first number is the map and the second is the ground, both in the same unit. On 1:50 000, 1 cm on the map is 50 000 cm on the ground.

Convert once and keep the result as a fact for that map: 50 000 cm = 500 m. So on a 1:50 000 map, 1 cm stands for 500 m, and 2 cm for 1 000 m.

How do you convert a map distance, step by step?

1. Measure the map distance in cm, along the line the question names.
2. Multiply by the scale number to get the real distance in cm.
3. Convert to the unit the question asks for: divide by 100 for metres, by 100 000 for kilometres.
4. Check that the answer is sensible for the place. A village street should not come out at 400 km.

For the reverse, divide the real distance (in cm) by the scale number to get the map distance.

Worked example

The numbers here are invented for practice. A map has a scale of 1:50 000.

The road from a school to a bridge measures 7.4 cm on the map. Find the real distance in km.

Step 1: map distance = 7.4 cm.

Step 2: 7.4 × 50 000 = 370 000 cm.

Step 3: 370 000 ÷ 100 = 3 700 m, and 3 700 ÷ 1 000 = 3.7 km.

Check: 1 cm is 0.5 km, and 7.4 × 0.5 = 3.7 km. Both routes agree.

Reverse question: a footpath is 2.5 km long. How long is it on a 1:25 000 map? 2.5 km = 250 000 cm, and 250 000 ÷ 25 000 = 10 cm. Check: 1 cm is 250 m on this map, and 2 500 ÷ 250 = 10.

The mistake to watch for

Mistaken answer: 7.4 × 50 000 = 370 000, so the distance is 370 000 km.

The student multiplied correctly but forgot that the result is in centimetres.

The number is right and the unit is wrong. A road of 370 000 km would be roughly the distance from the Earth to the Moon, which is the kind of check that catches it.

Fix it by writing the unit on every line. After the multiplication write “cm”, then convert in two labelled steps.

Check yourself

1. The scale is 1:100 000. Two towns are 4.6 cm apart on the map. How far apart are they in km?

2. The scale is 1:25 000. A river bend measures 6 cm along the map. What is the real length in km?

3. A coastal path is 12 km long. How long is it on a 1:200 000 map?

Where this leads next

Next, see why area scales by the square, then try the scale and relief practice set. The map scale, contour and gradient practice tool lets you rehearse conversions with fresh numbers.

If conversions are still the weak point across several topics, our teachers can look at them with you in online one-to-one Geography tuition.